留言板

尊敬的讀者、作者、審稿人, 關于本刊的投稿、審稿、編輯和出版的任何問題, 您可以本頁添加留言。我們將盡快給您答復。謝謝您的支持!

姓名
郵箱
手機號碼
標題
留言內容
驗證碼

含雙自由度周期振子的平行并聯梁彎曲振動帶隙特性

丁蘭 丁彪 吳巧云 朱宏平

丁蘭, 丁彪, 吳巧云, 朱宏平. 含雙自由度周期振子的平行并聯梁彎曲振動帶隙特性[J]. 工程力學, 2023, 40(10): 1-10, 57. doi: 10.6052/j.issn.1000-4750.2022.01.0086
引用本文: 丁蘭, 丁彪, 吳巧云, 朱宏平. 含雙自由度周期振子的平行并聯梁彎曲振動帶隙特性[J]. 工程力學, 2023, 40(10): 1-10, 57. doi: 10.6052/j.issn.1000-4750.2022.01.0086
DING Lan, DING Biao, WU Qiao-yun, ZHU Hong-ping. FLEXURAL VIBRATION BANDGAP CHARACTERISTICS OF DOUBLE BEAMS IN PARALLEL WITH OSCILLATORS WITH TWO DEGREES OF FREEDOM[J]. Engineering Mechanics, 2023, 40(10): 1-10, 57. doi: 10.6052/j.issn.1000-4750.2022.01.0086
Citation: DING Lan, DING Biao, WU Qiao-yun, ZHU Hong-ping. FLEXURAL VIBRATION BANDGAP CHARACTERISTICS OF DOUBLE BEAMS IN PARALLEL WITH OSCILLATORS WITH TWO DEGREES OF FREEDOM[J]. Engineering Mechanics, 2023, 40(10): 1-10, 57. doi: 10.6052/j.issn.1000-4750.2022.01.0086

含雙自由度周期振子的平行并聯梁彎曲振動帶隙特性

doi: 10.6052/j.issn.1000-4750.2022.01.0086
基金項目: 國家自然科學基金項目(51908521,52078395,51838006)
詳細信息
    作者簡介:

    丁 蘭(1985?),女,湖北人,副教授,博士,主要從事結構振動分析與控制研究(E-mail: dinglan@cug.edu.cn)

    丁 彪(1998?),男,山東人,碩士生,主要從事周期結構振動控制研究(E-mail: dingbiao@cug.edu.cn)

    朱宏平(1965?),男,湖北人,教授,博士,博導,主要從事結構抗震、損傷識別及健康檢測研究(E-mail: hpzhu@mail.hust.edu.cn)

    通訊作者:

    吳巧云(1985?),女,山東人,教授,博士,主要從事結構抗震研究(E-mail: wuqiaoyun@wit.edu.cn)

  • 中圖分類號: TU352

FLEXURAL VIBRATION BANDGAP CHARACTERISTICS OF DOUBLE BEAMS IN PARALLEL WITH OSCILLATORS WITH TWO DEGREES OF FREEDOM

  • 摘要: 為探究新型周期結構的低頻多帶隙特性,提出了周期布置雙自由度振子的局域共振型平行并聯梁結構。利用平面波展開法,計算了無限周期結構的彎曲振動能帶結構。采用有限元法計算了有限周期結構的振動傳輸曲線,并通過模態分析和變形模式研究了帶隙產生機理。建立了雙自由振子并聯梁的簡化模型,推導了帶隙起止頻率簡化公式,研究了結構參數對帶隙特性的影響規律。最后制作了模型試件并進行傳遞特性分析,驗證了理論和有限元法預測帶隙的準確性。研究表明,僅改變兩梁之間連接彈簧的剛度,可以有效調節帶隙頻率,為雙自由度振子雙梁周期結構的減振控制提供參考。
  • 圖  1  含周期振子的平行并聯梁模型示意圖

    Figure  1.  Schematic model of two beams in parallel with periodic oscillators

    圖  2  并聯周期梁結構的能帶結構和傳輸特性圖(T代表同側傳輸特性,Y代表異側傳輸特性)

    Figure  2.  Band structure and transmission property of the periodic beams in parallel

    圖  3  使用彈簧連接的平行并聯周期梁模型示意圖

    Figure  3.  Schematic model of the two beams connected with springs

    圖  4  使用彈簧連接的并聯周期梁結構能帶結構和傳輸特性圖

    Figure  4.  Band structure and transmission property of the two beams connected with springs

    圖  5  平行并聯梁晶胞單元固有模態圖

    Figure  5.  Eigenmodes of the unit cell

    圖  6  有限周期結構在不同頻率下的振動變形圖

    Figure  6.  Deformation of the finite periodic structure

    圖  7  f21頻率處彈簧振子模型示意圖

    Figure  7.  Simple model of the spring-mass-beam at f21

    圖  8  f3頻率處彈簧振子模型示意圖

    Figure  8.  Simple model of the spring-mass-beam at f3

    圖  9  f4頻率處彈簧振子模型示意圖

    Figure  9.  Simple model of the spring-mass-beam at f4

    圖  10  帶隙隨a、k1m變化圖

    Figure  10.  Effects of a, k1 and m on the bandgap

    圖  11  彈簧連接剛度變化對能帶結構和帶隙頻率的影響

    Figure  11.  Effects of the stiffness of the connected springs on the band structure and bandgap

    圖  12  模型試件測試系統圖

    Figure  12.  Experiment system of the model

    圖  13  試驗和有限元仿真計算振動傳輸特性

    Figure  13.  Transmission properties by experiment and finite element method

    表  1  材料參數表

    Table  1.   Material properties

    材料密度ρ/(kg·m?3)彈性模量E/(×109 Pa)泊松比μ
    2600700.30
    78602060.27
    下載: 導出CSV

    表  2  結構幾何參數表

    Table  2.   Geometrical properties

    晶格長度
    a/m
    梁寬b=
    梁高h/m
    彈簧剛度
    k1=k2/(kN·m?1)
    振子質量
    m/kg
    振子寬l1=
    振子高l2/m
    振子長
    l3/m
    0.060.01400.094320.020.03
    下載: 導出CSV

    黑人大屌丝逼逼
  • [1] 文岐華, 左曙光, 魏歡. 多振子梁彎曲振動中的局域共振帶隙[J]. 物理學報, 2012, 61(3): 240 ? 246. doi: 10.7498/aps.61.034301

    WEN Qihua, ZUO Shuguang, WEI Huan. Locally resonant elastic wave band gaps in flexural vibration of multi-oscillators beam [J]. Acta Physica Sinica, 2012, 61(3): 240 ? 246. (in Chinese) doi: 10.7498/aps.61.034301
    [2] 丁蘭, 朱宏平, 吳巧云. 彈性地基上隨機失諧周期加固管的波動局部化特性研究[J]. 工程力學, 2015, 32(2): 45 ? 52. doi: 10.6052/j.issn.1000-4750.2014.01.0036

    DING Lan, ZHU Hongping, WU Qiaoyun. Study on wave localization in randomly disordered periodically stiffened pipes on elastic foundations [J]. Engineering Mechanics, 2015, 32(2): 45 ? 52. (in Chinese) doi: 10.6052/j.issn.1000-4750.2014.01.0036
    [3] 馬建剛, 盛美萍, 韓玉迎. 多帶隙局域共振單元抑振設計與實驗驗證[J]. 振動工程學報, 2019, 32(6): 943 ? 949.

    MA Jiangang, SHENG Meiping, HAN Yuying. Structure design and experimental verification of multi-bandgap locally resonant unit [J]. Journal of Vibration Engineering, 2019, 32(6): 943 ? 949. (in Chinese)
    [4] 范重, 崔俊偉, 薛浩淳, 等. 地鐵上蓋結構隔震效果研究[J]. 工程力學, 2021, 38(增刊): 77 ? 88. doi: 10.6052/j.issn.1000-4750.2020.05.S015

    FAN Zhong, CUI Junwei, XUE Haochun, et al. Study on the isolation effect of subway cover structures [J]. Engineering Mechanics, 2021, 38(Suppl): 77 ? 88. (in Chinese) doi: 10.6052/j.issn.1000-4750.2020.05.S015
    [5] 葛倩倩, 于桂蘭. 有覆層土體中部分埋入式表面波屏障[J]. 工程力學, 2020, 37(增刊 1): 249 ? 253. doi: 10.6052/j.issn.1000-4750.2019.04.S046

    GE Qianqian, YU Guilan. A partially embedded periodic barrier for surface waves in soil with a covered layer [J]. Engineering Mechanics, 2020, 37(Suppl 1): 249 ? 253. (in Chinese) doi: 10.6052/j.issn.1000-4750.2019.04.S046
    [6] 郁殿龍. 基于聲子晶體理論的梁板類周期結構振動帶隙特性研究 [D]. 長沙: 國防科學技術大學, 2006: 1 ? 145

    YU Dianlong. Research on the vibration band gaps of periodic beams and plates based on the theory of phononic crystals [D]. Changsha: National University of Defense Technology, 2006: 1 ? 145. (in Chinese)
    [7] TIAN X Y, CHEN W J, GAO R J, et al. Merging Bragg and local resonance bandgaps in perforated elastic metamaterials with embedded spiral holes [J]. Journal of Sound and Vibration, 2021, 500: 116036. doi: 10.1016/j.jsv.2021.116036
    [8] ADRIEN P, THOMAS G, FRAN?OIS G. On the control of the first Bragg band gap in periodic continuously corrugated beam for flexural vibration [J]. Journal of Sound and Vibration, 2019, 446: 249 ? 262. doi: 10.1016/j.jsv.2019.01.029
    [9] GUO Z K, HU G B, SOROKIN V, et al. Low-frequency flexural wave attenuation in metamaterial sandwich beam with hourglass lattice truss core [J]. Wave Motion, 2021, 104: 102750. doi: 10.1016/j.wavemoti.2021.102750
    [10] HUSSEIN M I, LEAMY M J, RUZZEne M. Dynamics of phononic materials and structures: Historical origins, recent progress, and future outlook [J]. Applied Mechanics Reviews, 2014, 66(4): 040802. doi: 10.1115/1.4026911
    [11] 吳旭東, 左曙光, 倪天心, 等. 并聯雙振子聲子晶體梁結構帶隙特性研究[J]. 振動工程學報, 2017, 30(1): 79 ? 85. doi: 10.16385/j.cnki.issn.1004-4523.2017.01.011

    WU Xudong, ZUO Shuguang, NI Tianxin, et al. Study of the bandgap characteristics of a locally resonant phononic crystal beam with attached double oscillators in parallel [J]. Journal of Vibration Engineering, 2017, 30(1): 79 ? 85. (in Chinese) doi: 10.16385/j.cnki.issn.1004-4523.2017.01.011
    [12] WANG G, WEN J H, WEN X S. Quasi-one-dimensional phononic crystals studied using the improved lumped-mass method: Application to locally resonant beams with flexural wave band gap [J]. Physical Review B, 2005, 71(10): 104302. doi: 10.1103/PhysRevB.71.104302
    [13] XIAO Y, WEN J H, YU D L, et al. Flexural wave propagation in beams with periodically attached vibration absorbers: Band-gap behavior and band formation mechanisms [J]. Journal of Sound and Vibration, 2013, 332(4): 867 ? 893. doi: 10.1016/j.jsv.2012.09.035
    [14] YU D L, WEN J H, SHEN H J, et al. Propagation of ?exural wave in periodic beam on elastic foundations [J]. Physics Letters A, 2012, 376(4): 626 ? 630. doi: 10.1016/j.physleta.2011.11.056
    [15] HU G B, AUSTIN A C M, SOROKIN V, et al. Metamaterial beam with graded local resonators for broadband vibration suppression [J]. Mechanical Systems and Signal Processing, 2021, 146: 106982. doi: 10.1016/j.ymssp.2020.106982
    [16] YU D L, LIU Y Z, ZHAO H G, et al. Flexural vibration band gaps in Euler-Bernoulli beams with locally resonant structures with two degrees of freedom [J]. Physical Review B, 2006, 73(6): 064301.
    [17] WANG Z Y, ZHANG P, ZHANG Y Q. Locally resonant band gaps in flexural vibrations of a Timoshenko beam with periodically attached multioscillators [J]. Mathematical Problems in Engineering, 2013, 2013: 146975-1 ? 146975-10. doi: 10.1155/2013/146975
    [18] DING L, YE Z, WU Q Y. Flexural vibration band gaps in periodic Timoshenko beams with oscillators in series resting on flexible supports [J]. Advances in Structural Engineering, 2020, 23(14): 3117 ? 3127. doi: 10.1177/1369433220928529
    [19] CHEN J S, SHARMA B, SUN C T. Dynamic behaviour of sandwich structure containing spring-mass resonators [J]. Composite Structures, 2011, 93(8): 2120 ? 2125. doi: 10.1016/j.compstruct.2011.02.007
    [20] SHARMA B, SUN C T. Local resonance and Bragg bandgaps in sandwich beams containing periodically inserted resonators [J]. Journal of Sound and Vibration, 2016, 364: 133 ? 146. doi: 10.1016/j.jsv.2015.11.019
    [21] 涂靜, 史治宇. 雙層歐拉梁聲子晶體彎曲振動帶隙特性研究[J]. 機械制造與自動化, 2020, 49(2): 69 ? 73. doi: 10.19344/j.cnki.issn1671-5276.2020.02.017

    TU Jing, SHI Zhiyu. Study on bandgap characteristics of bending vibration of double-layer Euler beam phononic crystal [J]. Mechanical Manufacture and Automation, 2020, 49(2): 69 ? 73. (in Chinese) doi: 10.19344/j.cnki.issn1671-5276.2020.02.017
    [22] HE F Y, SHI Z Y, QIAN D H, et al. Flexural wave bandgap properties in metamaterial dual-beam structure [J]. Physics Letters A, 2022, 429: 127950. doi: 10.1016/j.physleta.2022.127950
    [23] CHEN J S, HUANG Y J. Wave propagation in sandwich structures with multiresonators [J]. Journal of Vibration and Acoustics, 2016, 138(4): 041009. doi: 10.1115/1.4033197
    [24] CHEN H, LI X P, CHEN Y Y, et al. Wave propagation and absorption of sandwich beams containing interior dissipative multi-resonators [J]. Ultrasonics, 2017, 76: 99 ? 108. doi: 10.1016/j.ultras.2016.12.014
    [25] ZHANG Y, FAN X L, LI J Q, et al. Low-frequency vibration insulation performance of the pyramidal lattice sandwich metamaterial beam [J]. Composite Structures, 2021, 278: 114719. doi: 10.1016/j.compstruct.2021.114719
  • 加載中
圖(13) / 表(2)
計量
  • 文章訪問數:  331
  • HTML全文瀏覽量:  141
  • PDF下載量:  83
  • 被引次數: 0
出版歷程
  • 收稿日期:  2022-01-18
  • 修回日期:  2022-05-18
  • 錄用日期:  2022-06-25
  • 網絡出版日期:  2022-06-25
  • 刊出日期:  2023-10-10

目錄

    /

    返回文章
    返回